arch/m68k/fpsp040/srem_mod.S

   1 |
   2 |       srem_mod.sa 3.1 12/10/90
   3 |
   4 |      The entry point sMOD computes the floating point MOD of the
   5 |      input values X and Y. The entry point sREM computes the floating
   6 |      point (IEEE) REM of the input values X and Y.
   7 |
   8 |      INPUT
   9 |      -----
  10 |      Double-extended value Y is pointed to by address in register
  11 |      A0. Double-extended value X is located in -12(A0). The values
  12 |      of X and Y are both nonzero and finite; although either or both
  13 |      of them can be denormalized. The special cases of zeros, NaNs,
  14 |      and infinities are handled elsewhere.
  15 |
  16 |      OUTPUT
  17 |      ------
  18 |      FREM(X,Y) or FMOD(X,Y), depending on entry point.
  19 |
  20 |       ALGORITHM
  21 |       ---------
  22 |
  23 |       Step 1.  Save and strip signs of X and Y: signX := sign(X),
  24 |                signY := sign(Y), X := |X|, Y := |Y|,
  25 |                signQ := signX EOR signY. Record whether MOD or REM
  26 |                is requested.
  27 |
  28 |       Step 2.  Set L := expo(X)-expo(Y), k := 0, Q := 0.
  29 |                If (L < 0) then
  30 |                   R := X, go to Step 4.
  31 |                else
  32 |                   R := 2^(-L)X, j := L.
  33 |                endif
  34 |
  35 |       Step 3.  Perform MOD(X,Y)
  36 |            3.1 If R = Y, go to Step 9.
  37 |            3.2 If R > Y, then { R := R - Y, Q := Q + 1}
  38 |            3.3 If j = 0, go to Step 4.
  39 |            3.4 k := k + 1, j := j - 1, Q := 2Q, R := 2R. Go to
  40 |                Step 3.1.
  41 |
  42 |       Step 4.  At this point, R = X - QY = MOD(X,Y). Set
  43 |                Last_Subtract := false (used in Step 7 below). If
  44 |                MOD is requested, go to Step 6.
  45 |
  46 |       Step 5.  R = MOD(X,Y), but REM(X,Y) is requested.
  47 |            5.1 If R < Y/2, then R = MOD(X,Y) = REM(X,Y). Go to
  48 |                Step 6.
  49 |            5.2 If R > Y/2, then { set Last_Subtract := true,
  50 |                Q := Q + 1, Y := signY*Y }. Go to Step 6.
  51 |            5.3 This is the tricky case of R = Y/2. If Q is odd,
  52 |                then { Q := Q + 1, signX := -signX }.
  53 |
  54 |       Step 6.  R := signX*R.
  55 |
  56 |       Step 7.  If Last_Subtract = true, R := R - Y.
  57 |
  58 |       Step 8.  Return signQ, last 7 bits of Q, and R as required.
  59 |
  60 |       Step 9.  At this point, R = 2^(-j)*X - Q Y = Y. Thus,
  61 |                X = 2^(j)*(Q+1)Y. set Q := 2^(j)*(Q+1),
  62 |                R := 0. Return signQ, last 7 bits of Q, and R.
  63 |
  64 |
  65
  66 |               Copyright (C) Motorola, Inc. 1990
  67 |                       All Rights Reserved
  68 |
  69 |       THIS IS UNPUBLISHED PROPRIETARY SOURCE CODE OF MOTOROLA
  70 |       The copyright notice above does not evidence any
  71 |       actual or intended publication of such source code.
  72
  73 SREM_MOD:    |idnt    2,1 | Motorola 040 Floating Point Software Package
  74
  75         |section    8
  76
  77 #include "fpsp.h"
  78
  79         .set    Mod_Flag,L_SCR3
  80         .set    SignY,FP_SCR3+4
  81         .set    SignX,FP_SCR3+8
  82         .set    SignQ,FP_SCR3+12
  83         .set    Sc_Flag,FP_SCR4
  84
  85         .set    Y,FP_SCR1
  86         .set    Y_Hi,Y+4
  87         .set    Y_Lo,Y+8
  88
  89         .set    R,FP_SCR2
  90         .set    R_Hi,R+4
  91         .set    R_Lo,R+8
  92
  93
  94 Scale:     .long        0x00010000,0x80000000,0x00000000,0x00000000
  95
  96         |xref   t_avoid_unsupp
  97
  98         .global        smod
  99 smod:
 100
 101    movel               #0,Mod_Flag(%a6)
 102    bras                Mod_Rem
 103
 104         .global        srem
 105 srem:
 106
 107    movel               #1,Mod_Flag(%a6)
 108
 109 Mod_Rem:
 110 |..Save sign of X and Y
 111    moveml              %d2-%d7,-(%a7)     | ...save data registers
 112    movew               (%a0),%d3
 113    movew               %d3,SignY(%a6)
 114    andil               #0x00007FFF,%d3   | ...Y := |Y|
 115
 116 |
 117    movel               4(%a0),%d4
 118    movel               8(%a0),%d5        | ...(D3,D4,D5) is |Y|
 119
 120    tstl                %d3
 121    bnes                Y_Normal
 122
 123    movel               #0x00003FFE,%d3  | ...$3FFD + 1
 124    tstl                %d4
 125    bnes                HiY_not0
 126
 127 HiY_0:
 128    movel               %d5,%d4
 129    clrl                %d5
 130    subil               #32,%d3
 131    clrl                %d6
 132    bfffo                %d4{#0:#32},%d6
 133    lsll                %d6,%d4
 134    subl                %d6,%d3           | ...(D3,D4,D5) is normalized
 135 |                                       ...with bias $7FFD
 136    bras                Chk_X
 137
 138 HiY_not0:
 139    clrl                %d6
 140    bfffo                %d4{#0:#32},%d6
 141    subl                %d6,%d3
 142    lsll                %d6,%d4
 143    movel               %d5,%d7           | ...a copy of D5
 144    lsll                %d6,%d5
 145    negl                %d6
 146    addil               #32,%d6
 147    lsrl                %d6,%d7
 148    orl                 %d7,%d4           | ...(D3,D4,D5) normalized
 149 |                                       ...with bias $7FFD
 150    bras                Chk_X
 151
 152 Y_Normal:
 153    addil               #0x00003FFE,%d3   | ...(D3,D4,D5) normalized
 154 |                                       ...with bias $7FFD
 155
 156 Chk_X:
 157    movew               -12(%a0),%d0
 158    movew               %d0,SignX(%a6)
 159    movew               SignY(%a6),%d1
 160    eorl                %d0,%d1
 161    andil               #0x00008000,%d1
 162    movew               %d1,SignQ(%a6)   | ...sign(Q) obtained
 163    andil               #0x00007FFF,%d0
 164    movel               -8(%a0),%d1
 165    movel               -4(%a0),%d2       | ...(D0,D1,D2) is |X|
 166    tstl                %d0
 167    bnes                X_Normal
 168    movel               #0x00003FFE,%d0
 169    tstl                %d1
 170    bnes                HiX_not0
 171
 172 HiX_0:
 173    movel               %d2,%d1
 174    clrl                %d2
 175    subil               #32,%d0
 176    clrl                %d6
 177    bfffo                %d1{#0:#32},%d6
 178    lsll                %d6,%d1
 179    subl                %d6,%d0           | ...(D0,D1,D2) is normalized
 180 |                                       ...with bias $7FFD
 181    bras                Init
 182
 183 HiX_not0:
 184    clrl                %d6
 185    bfffo                %d1{#0:#32},%d6
 186    subl                %d6,%d0
 187    lsll                %d6,%d1
 188    movel               %d2,%d7           | ...a copy of D2
 189    lsll                %d6,%d2
 190    negl                %d6
 191    addil               #32,%d6
 192    lsrl                %d6,%d7
 193    orl                 %d7,%d1           | ...(D0,D1,D2) normalized
 194 |                                       ...with bias $7FFD
 195    bras                Init
 196
 197 X_Normal:
 198    addil               #0x00003FFE,%d0   | ...(D0,D1,D2) normalized
 199 |                                       ...with bias $7FFD
 200
 201 Init:
 202 |
 203    movel               %d3,L_SCR1(%a6)   | ...save biased expo(Y)
 204    movel                %d0,L_SCR2(%a6) |save d0
 205    subl                %d3,%d0           | ...L := expo(X)-expo(Y)
 206 |   Move.L               D0,L            ...D0 is j
 207    clrl                %d6              | ...D6 := carry <- 0
 208    clrl                %d3              | ...D3 is Q
 209    moveal              #0,%a1           | ...A1 is k; j+k=L, Q=0
 210
 211 |..(Carry,D1,D2) is R
 212    tstl                %d0
 213    bges                Mod_Loop
 214
 215 |..expo(X) < expo(Y). Thus X = mod(X,Y)
 216 |
 217    movel                L_SCR2(%a6),%d0 |restore d0
 218    bra                Get_Mod
 219
 220 |..At this point  R = 2^(-L)X; Q = 0; k = 0; and  k+j = L
 221
 222
 223 Mod_Loop:
 224    tstl                %d6              | ...test carry bit
 225    bgts                R_GT_Y
 226
 227 |..At this point carry = 0, R = (D1,D2), Y = (D4,D5)
 228    cmpl                %d4,%d1           | ...compare hi(R) and hi(Y)
 229    bnes                R_NE_Y
 230    cmpl                %d5,%d2           | ...compare lo(R) and lo(Y)
 231    bnes                R_NE_Y
 232
 233 |..At this point, R = Y
 234    bra                Rem_is_0
 235
 236 R_NE_Y:
 237 |..use the borrow of the previous compare
 238    bcss                R_LT_Y          | ...borrow is set iff R < Y
 239
 240 R_GT_Y:
 241 |..If Carry is set, then Y < (Carry,D1,D2) < 2Y. Otherwise, Carry = 0
 242 |..and Y < (D1,D2) < 2Y. Either way, perform R - Y
 243    subl                %d5,%d2           | ...lo(R) - lo(Y)
 244    subxl               %d4,%d1           | ...hi(R) - hi(Y)
 245    clrl                %d6              | ...clear carry
 246    addql               #1,%d3           | ...Q := Q + 1
 247
 248 R_LT_Y:
 249 |..At this point, Carry=0, R < Y. R = 2^(k-L)X - QY; k+j = L; j >= 0.
 250    tstl                %d0              | ...see if j = 0.
 251    beqs                PostLoop
 252
 253    addl                %d3,%d3           | ...Q := 2Q
 254    addl                %d2,%d2           | ...lo(R) = 2lo(R)
 255    roxll               #1,%d1           | ...hi(R) = 2hi(R) + carry
 256    scs                  %d6              | ...set Carry if 2(R) overflows
 257    addql               #1,%a1           | ...k := k+1
 258    subql               #1,%d0           | ...j := j - 1
 259 |..At this point, R=(Carry,D1,D2) = 2^(k-L)X - QY, j+k=L, j >= 0, R < 2Y.
 260
 261    bras                Mod_Loop
 262
 263 PostLoop:
 264 |..k = L, j = 0, Carry = 0, R = (D1,D2) = X - QY, R < Y.
 265
 266 |..normalize R.
 267    movel               L_SCR1(%a6),%d0           | ...new biased expo of R
 268    tstl                %d1
 269    bnes                HiR_not0
 270
 271 HiR_0:
 272    movel               %d2,%d1
 273    clrl                %d2
 274    subil               #32,%d0
 275    clrl                %d6
 276    bfffo                %d1{#0:#32},%d6
 277    lsll                %d6,%d1
 278    subl                %d6,%d0           | ...(D0,D1,D2) is normalized
 279 |                                       ...with bias $7FFD
 280    bras                Get_Mod
 281
 282 HiR_not0:
 283    clrl                %d6
 284    bfffo                %d1{#0:#32},%d6
 285    bmis                Get_Mod         | ...already normalized
 286    subl                %d6,%d0
 287    lsll                %d6,%d1
 288    movel               %d2,%d7           | ...a copy of D2
 289    lsll                %d6,%d2
 290    negl                %d6
 291    addil               #32,%d6
 292    lsrl                %d6,%d7
 293    orl                 %d7,%d1           | ...(D0,D1,D2) normalized
 294
 295 |
 296 Get_Mod:
 297    cmpil                #0x000041FE,%d0
 298    bges         No_Scale
 299 Do_Scale:
 300    movew                %d0,R(%a6)
 301    clrw         R+2(%a6)
 302    movel                %d1,R_Hi(%a6)
 303    movel                %d2,R_Lo(%a6)
 304    movel                L_SCR1(%a6),%d6
 305    movew                %d6,Y(%a6)
 306    clrw         Y+2(%a6)
 307    movel                %d4,Y_Hi(%a6)
 308    movel                %d5,Y_Lo(%a6)
 309    fmovex               R(%a6),%fp0             | ...no exception
 310    movel                #1,Sc_Flag(%a6)
 311    bras         ModOrRem
 312 No_Scale:
 313    movel                %d1,R_Hi(%a6)
 314    movel                %d2,R_Lo(%a6)
 315    subil                #0x3FFE,%d0
 316    movew                %d0,R(%a6)
 317    clrw         R+2(%a6)
 318    movel                L_SCR1(%a6),%d6
 319    subil                #0x3FFE,%d6
 320    movel                %d6,L_SCR1(%a6)
 321    fmovex               R(%a6),%fp0
 322    movew                %d6,Y(%a6)
 323    movel                %d4,Y_Hi(%a6)
 324    movel                %d5,Y_Lo(%a6)
 325    movel                #0,Sc_Flag(%a6)
 326
 327 |
 328
 329
 330 ModOrRem:
 331    movel               Mod_Flag(%a6),%d6
 332    beqs                Fix_Sign
 333
 334    movel               L_SCR1(%a6),%d6           | ...new biased expo(Y)
 335    subql               #1,%d6           | ...biased expo(Y/2)
 336    cmpl                %d6,%d0
 337    blts                Fix_Sign
 338    bgts                Last_Sub
 339
 340    cmpl                %d4,%d1
 341    bnes                Not_EQ
 342    cmpl                %d5,%d2
 343    bnes                Not_EQ
 344    bra                Tie_Case
 345
 346 Not_EQ:
 347    bcss                Fix_Sign
 348
 349 Last_Sub:
 350 |
 351    fsubx                Y(%a6),%fp0             | ...no exceptions
 352    addql               #1,%d3           | ...Q := Q + 1
 353
 354 |
 355
 356 Fix_Sign:
 357 |..Get sign of X
 358    movew               SignX(%a6),%d6
 359    bges         Get_Q
 360    fnegx                %fp0
 361
 362 |..Get Q
 363 |
 364 Get_Q:
 365    clrl         %d6
 366    movew               SignQ(%a6),%d6        | ...D6 is sign(Q)
 367    movel               #8,%d7
 368    lsrl                %d7,%d6
 369    andil               #0x0000007F,%d3   | ...7 bits of Q
 370    orl                 %d6,%d3           | ...sign and bits of Q
 371    swap                 %d3
 372    fmovel              %fpsr,%d6
 373    andil               #0xFF00FFFF,%d6
 374    orl                 %d3,%d6
 375    fmovel              %d6,%fpsr         | ...put Q in fpsr
 376
 377 |
 378 Restore:
 379    moveml              (%a7)+,%d2-%d7
 380    fmovel              USER_FPCR(%a6),%fpcr
 381    movel               Sc_Flag(%a6),%d0
 382    beqs                Finish
 383    fmulx                Scale(%pc),%fp0 | ...may cause underflow
 384    bra                  t_avoid_unsupp  |check for denorm as a
 385 |                                       ;result of the scaling
 386
 387 Finish:
 388         fmovex          %fp0,%fp0               |capture exceptions & round
 389         rts
 390
 391 Rem_is_0:
 392 |..R = 2^(-j)X - Q Y = Y, thus R = 0 and quotient = 2^j (Q+1)
 393    addql               #1,%d3
 394    cmpil               #8,%d0           | ...D0 is j
 395    bges                Q_Big
 396
 397    lsll                %d0,%d3
 398    bras                Set_R_0
 399
 400 Q_Big:
 401    clrl                %d3
 402
 403 Set_R_0:
 404    fmoves               #0x00000000,%fp0
 405    movel                #0,Sc_Flag(%a6)
 406    bra                Fix_Sign
 407
 408 Tie_Case:
 409 |..Check parity of Q
 410    movel               %d3,%d6
 411    andil               #0x00000001,%d6
 412    tstl                %d6
 413    beq                Fix_Sign  | ...Q is even
 414
 415 |..Q is odd, Q := Q + 1, signX := -signX
 416    addql               #1,%d3
 417    movew               SignX(%a6),%d6
 418    eoril               #0x00008000,%d6
 419    movew               %d6,SignX(%a6)
 420    bra                Fix_Sign
 421
 422    |end